Finite Group Databasebeta

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C₂³×C₃×C₁₃×C₁₉ #72185142

order	5928
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 72576
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂³×C₃×C₁₃×C₁₉
multiplicative	(ℤ/11864)ˣ, (ℤ/17796)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5928 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₃×C₁₃×C₁₉, C₂²×C₃×C₄×C₁₃×C₁₉, C₂³×C₉×C₁₃×C₁₉, …
maximal normal subgroup of	C₂⁴×C₃×C₁₃×C₁₉, C₂²×C₃×C₄×C₁₃×C₁₉, C₂³×C₉×C₁₃×C₁₉, …
maximal quotient of	C₂⁴×C₃×C₁₃×C₁₉, C₂²×C₃×C₄×C₁₃×C₁₉, C₂³×C₉×C₁₃×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.